Earlier quoted context omitted.
Sexism != reacting to the sexes differently. Men and women are not the same, and therefore they evoke different responses and reactions. This is not sexism.
That's exactly what sexism is. It's not always necessarily a bad thing.
No, it is not. Sexism, like racism, never has a positive or neutral connotation in any context in which I have ever heard it used. A black man is not intrinsically different than a white man. Therefore, to treat him such is racist, period. A woman is, however, intrinsically different than a man. To denigrate her because she is a women is sexism. To treat her as if she were a man and refuse to acknowledge her as a woman is, arguably, also sexism. On the contrary, merely to react differently to her, but not negatively, is not sexism.